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We propose and analyze an approach for fast syndrome measurements in an array of rubidium and cesium atomic qubits. The scheme works by implementing an inter-species $\textsf{CNOT}_k$ gate, entangling one cesium ancilla qubit with $k\geq 1$ rubidium qubits which are then used for state measurement. Utilizing Rydberg states with different inter- and intra-species interaction strengths, the proposal provides a syndrome measurement fidelity of $\mathcal{F}>0.9999$ in less than 5 $\mu$s of integration time.

We propose an implementation of bivariate bicycle codes (Nature {\bf 627}, 778 (2024)) based on long-range Rydberg gates between stationary neutral atom qubits. An optimized layout of data and ancilla qubits reduces the maximum Euclidean communication distance needed for non-local parity check operators. An optimized Rydberg gate pulse design enables $\sf CZ$ entangling operations with fidelity ${\mathcal F}>0.999$ at a distance greater than $12~\mu\rm m$. The combination of optimized layout and gate design leads to a quantum error correction cycle time of $\sim 1.2~\rm ms$ for a $[[144,12,12]]$ code, an order of magnitude improvement over previous designs.

In this study, we simulated the algorithmic performance of a small neutral atom quantum computer and compared its performance when operating with all-to-all versus nearest-neighbor connectivity. This comparison was made using a suite of algorithmic benchmarks developed by the Quantum Economic Development Consortium. Circuits were simulated with a noise model consistent with experimental data from Nature 604, 457 (2022). We find that all-to-all connectivity improves simulated circuit fidelity by $10\%-15\%$, compared to nearest-neighbor connectivity.

We demonstrate mid-circuit measurements in a neutral atom array by shelving data qubits in protected hyperfine-Zeeman sub-states while non-destructively measuring an ancilla qubit. Measurement fidelity was enhanced using microwave repumping of the ancilla during the measurement. The coherence of the shelved data qubits was extended during the ancilla readout with dynamical decoupling pulses, after which the data qubits are returned to mf = 0 computational basis states. We demonstrate that the quantum state of the data qubits is well preserved up to a constant phase shift with a state preparation and measurement (SPAM) corrected process fidelity of F = 97.0(5)%. The measurement fidelity on the ancilla qubit after correction for state preparation errors is F = 94.9(8)% and F = 95.3(1.1)% for |0> and |1> qubit states, respectively. We discuss extending this technique to repetitive quantum error correction using quadrupole recooling and microwave-based quantum state resetting., Comment: v3: additional appendices with fidelity analysis added

Gate model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high fidelity logic. Neutral atom hyperfine qubits provide inherent scalability due to their identical characteristics, long coherence times, and ability to be trapped in dense multi-dimensional arrays\cite{Saffman2010}. Combined with the strong entangling interactions provided by Rydberg states\cite{Jaksch2000,Gaetan2009,Urban2009}, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate model neutral atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states\cite{Greenberger1989} with up to 6 qubits, quantum phase estimation for a chemistry problem\cite{Aspuru-Guzik2005}, and the Quantum Approximate Optimization Algorithm (QAOA)\cite{Farhi2014} for the MaxCut graph problem are demonstrated. These results highlight the emergent capability of neutral atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum enhanced sensing., Comment: 4 figures and supplemental material. V2 details on phase estimation and RB data included

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit connectivity will constrain achievable circuit depth in the near future, new ways to achieve high-performance at low depth are of great interest. In this work, we present a modification to QAOA that adds additional variational parameters in the form of freedom of the rotation-axis in the $XY$-plane of the mixer Hamiltonian. Via numerical simulation, we show that this leads to a drastic performance improvement over standard QAOA at finding solutions to the MAXCUT problem on graphs of up to 7 qubits. Furthermore, we explore the Z-phase error mitigation properties of our modified ansatz, its performance under a realistic error model for a neutral atom quantum processor, and the class of problems it can solve in a single round., Comment: 8 pages, 4 figures, 3 pages and 5 figures supplementary

Atomic nuclei are important laboratories for exploring and testing new insights into the universe, such as experiments to directly detect dark matter or explore properties of neutrinos. The targets of interest are often heavy, complex nuclei that challenge our ability to reliably model them (as well as quantify the uncertainty of those models) with classical computers. Hence there is great interest in applying quantum computation to nuclear structure for these applications. As an early step in this direction, especially with regards to the uncertainties in the relevant quantum calculations, we develop circuits to implement variational quantum eigensolver (VQE) algorithms for the Lipkin-Meshkov-Glick model, which is often used in the nuclear physics community as a testbed for many-body methods. We present quantum circuits for VQE for two and three particles and discuss the construction of circuits for more particles. Implementing the VQE for a two-particle system on the IBM Quantum Experience, we identify initialization and two-qubit gates as the largest sources of error. We find that error mitigation procedures reduce the errors in the results significantly, but additional quantum hardware improvements are needed for quantum calculations to be sufficiently accurate to be competitive with the best current classical methods., Comment: 11 pages of RevTeX, 8 figures

The treatment of $\gamma_{5}$ in Dimensional Regularization leads to ambiguities in field-theoretic calculations, of which one example is the coefficient of a particular term in the four-loop gauge $\beta$-functions of the Standard Model. Using Weyl Consistency Conditions, we present a scheme-independent relation between the coefficient of this term and a corresponding term in the three-loop Yukawa $\beta$-functions, where a semi-na\"ive treatment of $\gamma_{5}$ is sufficient, thereby fixing this ambiguity. We briefly outline an argument by which the same method fixes similar ambiguities at higher orders., Comment: 9 pages, 3 figures. Version 2 notation updated to match Ref. [16], text expanded, calculation details clarified, conclusions unaffected

We provide an analysis of the structure of renormalisation scheme invariants for the case of $\phi^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at five loops, showing that there are considerably more invariants than one might naively have expected. We also show that one-vertex reducible contributions may consistently be omitted in a well-defined class of schemes which of course includes MSbar., Comment: Uses tikz; revised version with minor errors corrected

We have developed a new fully anisotropic 3D FDTD Maxwell solver for arbitrary electrically and magnetically anisotropic media for piecewise constant electric and magnetic materials that are co-located over the primary computational cells. Two numerical methods were developed that are called non-averaged and averaged methods, respectively. The non-averaged method is first order accurate, while the averaged method is second order accurate for smoothly-varying materials and reduces to first order for discontinuous material distributions. For the standard FDTD field locations with the co-location of the electric and magnetic materials at the primary computational cells, the averaged method require development of the different inversion algorithms of the constitutive relations for the electric and magnetic fields. We provide a mathematically rigorous stability proof followed by extensive numerical testing that includes long-time integration, eigenvalue analysis, tests with extreme, randomly placed material parameters, and various boundary conditions. For accuracy evaluation we have constructed a test case with an explicit analytic solution. Using transformation optics, we have constructed complex, spatially inhomogeneous geometrical object with fully anisotropic materials and a large dynamic range of $\underline{\epsilon}$ and $\underline{\mu}$, such that a plane wave incident on the object is perfectly reconstructed downstream. In our implementation, the considerable increase in accuracy of the averaged method only increases the computational run time by 20%.

Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops., Comment: 19 pages, uses Axodraw; revised version with reference added and typo in Eq.(3.9) corrected

Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and shown to be related to the beta-functions by a gradient flow equation with positive-definite metric as in four dimensions. Here, we extend this lowest-order calculation to a general abelian Chern-Simons gauge theory coupled to fermions and scalars, and derive a prediction for part of the four-loop Yukawa beta-function. We also compute the complete four-loop Yukawa beta-function for the scalar-fermion theory and show that it is entirely consistent with the gradient flow equations at next-to-leading order., Comment: 24 pages; uses Axodraw. Revised version with typos corrected

Non-minimal renormalisation schemes such as the momentum subtraction scheme (MOM) have frequently been used for physical computations. The consistency of such a scheme relies on the existence of a coupling redefinition linking it to MSbar. We discuss the implementation of this procedure in detail for a general theory and show how to construct the relevant redefinition up to three-loop order, for the case of a general theory of fermions and scalars in four dimensions and a general scalar theory in six dimensions., Comment: 24 pages,7 figures, uses axodraw

The a-function is a proposed quantity defined in even dimensions which has a monotonic behaviour along RG flows, related to the beta-functions via a gradient flow equation. We study the a-function for a general scalar theory in six dimensions, using the beta-functions up to three-loop order for both the MSbar and MOM schemes (the latter presented here for the first time at three loops)., Comment: 27 pages, seven figures, uses axodraw. Minor improvements in wording

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We demonstrate the existence of a candidate a-function for renormalisable Chern-Simons theories in three dimensions, involving scalar and fermion fields, in both non-supersymmetric and supersymmetric cases., Comment: 15 pages, 2 figures, uses axodraw. Revised with minor corrections; also additional clarifications and references included

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We construct the a-function at four loop order for a general gauge theory with fermions and scalars, using only one and two loop beta-functions; we are then able to provide a stringent consistency check on the general three-loop gauge beta-function. In the case of an N=1 supersymmetric gauge theory, we present a general condition on the chiral field anomalous dimension which guarantees an exact all-orders expression for the a-function; and we verify this up to fifth order (corresponding to the three-loop anomalous dimension)., Comment: 28 pages; uses axodraw; typos corrected, also some sign errors corrected in Sect 5

We extend the low-energy effective two-band Hamiltonian for electrons in bilayer graphene (E. McCann, V. I. Fal'ko, Phys. Rev. Lett. 96 (2006) 86805) to include a spatially dependent electrostatic potential. We find that this Hamiltonian contains additional terms, as compared to the one used earlier in the analysis of electronic transport in n-p junctions in bilayers (M. I. Katsnelson et al., Nat. Phys. 2 (2006) 620-625). However, for potential steps |u| < \gamma_1 (where \gamma_1 is the interlayer coupling), the corrections to the transmission probability due to such terms are small. For the angle-dependent transmission T (\theta) we find T (\theta) ~= sin^2(2 \theta) - (2 u/ 3 \gamma_1) sin(4 \theta) sin(\theta), which slightly increases the Fano factor: F ~= 0.241 for u = 40 meV., Comment: 4 pages, 5 figures. To be published in Solid State Communications